We present an iterative algorithm for approximating an unknown function sequentially using random samples of the function values and gradients. This is an extension of the recently developed sequential approximation (...We present an iterative algorithm for approximating an unknown function sequentially using random samples of the function values and gradients. This is an extension of the recently developed sequential approximation (SA) method, which approximates a target function using samples of function values only. The current paper extends the development of the SA methods to the Sobolev space and allows the use of gradient information naturally. The algorithm is easy to implement, as it requires only vector operations and does not involve any matrices. We present tight error bound of the algorithm, and derive an optimal sampling probability measure that results in fastest error convergence. Numerical examples are provided to verify the theoretical error analysis and the effectiveness of the proposed SA algorithm.展开更多
According to a lot of practical data in Liujialiang Mine and reliability theory and result of computer simulation, operation regularity of fully mechanized sublevel caving mining production system in the condition of ...According to a lot of practical data in Liujialiang Mine and reliability theory and result of computer simulation, operation regularity of fully mechanized sublevel caving mining production system in the condition of gently inclined complicated geological structure and production shortcomings are found out and reliability of system and output of the working face are predicted finally.展开更多
A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different ...A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.展开更多
This paper expounds the basic principles and structures of the whole petroleum system to reveal the pattern of conventional oil/gas-tight oil/gas-shale oil/gas sequential accumulation and the hydrocarbon accumulation ...This paper expounds the basic principles and structures of the whole petroleum system to reveal the pattern of conventional oil/gas-tight oil/gas-shale oil/gas sequential accumulation and the hydrocarbon accumulation models and mechanisms of the whole petroleum system.It delineates the geological model,flow model,and production mechanism of shale and tight reservoirs,and proposes future research orientations.The main structure of the whole petroleum system includes three fluid dynamic fields,three types of oil and gas reservoirs/resources,and two types of reservoir-forming processes.Conventional oil/gas,tight oil/gas,and shale oil/gas are orderly in generation time and spatial distribution,and sequentially rational in genetic mechanism,showing the pattern of sequential accumulation.The whole petroleum system involves two categories of hydrocarbon accumulation models:hydrocarbon accumulation in the detrital basin and hydrocarbon accumulation in the carbonate basin/formation.The accumulation of unconventional oil/gas is self-containment,which is microscopically driven by the intermolecular force(van der Waals force).The unconventional oil/gas production has proved that the geological model,flow model,and production mechanism of shale and tight reservoirs represent a new and complex field that needs further study.Shale oil/gas must be the most important resource replacement for oil and gas resources of China.Future research efforts include:(1)the characteristics of the whole petroleum system in carbonate basins and the source-reservoir coupling patterns in the evolution of composite basins;(2)flow mechanisms in migration,accumulation,and production of shale oil/gas and tight oil/gas;(3)geological characteristics and enrichment of deep and ultra-deep shale oil/gas,tight oil/gas and coalbed methane;(4)resource evaluation and new generation of basin simulation technology of the whole petroleum system;(5)research on earth system-earth organic rock and fossil fuel system-whole petroleum system.展开更多
文摘We present an iterative algorithm for approximating an unknown function sequentially using random samples of the function values and gradients. This is an extension of the recently developed sequential approximation (SA) method, which approximates a target function using samples of function values only. The current paper extends the development of the SA methods to the Sobolev space and allows the use of gradient information naturally. The algorithm is easy to implement, as it requires only vector operations and does not involve any matrices. We present tight error bound of the algorithm, and derive an optimal sampling probability measure that results in fastest error convergence. Numerical examples are provided to verify the theoretical error analysis and the effectiveness of the proposed SA algorithm.
文摘According to a lot of practical data in Liujialiang Mine and reliability theory and result of computer simulation, operation regularity of fully mechanized sublevel caving mining production system in the condition of gently inclined complicated geological structure and production shortcomings are found out and reliability of system and output of the working face are predicted finally.
文摘A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.
基金Supported by the National Natural Science Foundation of China(U22B6002)PetroChina Science Research and Technology Development Project(2021DJ0101)。
文摘This paper expounds the basic principles and structures of the whole petroleum system to reveal the pattern of conventional oil/gas-tight oil/gas-shale oil/gas sequential accumulation and the hydrocarbon accumulation models and mechanisms of the whole petroleum system.It delineates the geological model,flow model,and production mechanism of shale and tight reservoirs,and proposes future research orientations.The main structure of the whole petroleum system includes three fluid dynamic fields,three types of oil and gas reservoirs/resources,and two types of reservoir-forming processes.Conventional oil/gas,tight oil/gas,and shale oil/gas are orderly in generation time and spatial distribution,and sequentially rational in genetic mechanism,showing the pattern of sequential accumulation.The whole petroleum system involves two categories of hydrocarbon accumulation models:hydrocarbon accumulation in the detrital basin and hydrocarbon accumulation in the carbonate basin/formation.The accumulation of unconventional oil/gas is self-containment,which is microscopically driven by the intermolecular force(van der Waals force).The unconventional oil/gas production has proved that the geological model,flow model,and production mechanism of shale and tight reservoirs represent a new and complex field that needs further study.Shale oil/gas must be the most important resource replacement for oil and gas resources of China.Future research efforts include:(1)the characteristics of the whole petroleum system in carbonate basins and the source-reservoir coupling patterns in the evolution of composite basins;(2)flow mechanisms in migration,accumulation,and production of shale oil/gas and tight oil/gas;(3)geological characteristics and enrichment of deep and ultra-deep shale oil/gas,tight oil/gas and coalbed methane;(4)resource evaluation and new generation of basin simulation technology of the whole petroleum system;(5)research on earth system-earth organic rock and fossil fuel system-whole petroleum system.
